Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 4 - Section 4.2 - The Parallelogram and Kite - Exercises - Page 186: 37


The concave kite ( dart ) consists of two congruent triangle with an interior diagonal DB thus $ \triangle DBA= \triangle DBC $ by SSS And the interior diagonal BD also bisects angle D and B. measure of $ \triangle DBA = measure \triangle DBC= 180^{\circ} $ In $ \triangle DBC = \angle C + \angle DBC + \angle CDB = 30+ 15 + \angle DBC = 180 $ $ Thus \angle DBC= 120 $. Same procedure can be follow in the triangle DBC since they are congruent $Thus \angle DBA= 120^{\circ}$ Last step : since the reflex angle $ \angle B = \angle DBC + \angle DBA= 240^{\circ}$ Note : since the concave kite or ( dart ) in not a convex polygon its a concave polygon the corollary 2.5.4 cannot be applied on the concave polygon case.

Work Step by Step

m$\angle$B=360-m$\angle$A-m$\angle$C-m$\angle$D m$\angle$B=360-30-30-30 m$\angle$B=270$^{\circ}$
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